Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

learn more… | top users | synonyms (2)

4
votes
3answers
62 views

What is the meaning of percentile?

I am confused by the term percentile. Once my teacher told me that percentile means the percentage with respect to the score of the highest achiever. This means that if in a competition I got $80$ ...
1
vote
1answer
41 views

Venn diagram for a relation

My high school math book says the following diagram is a Venn diagram. But I think this is not correct. Is it right? If not, what is the following diagram that represents a relationship called?
1
vote
2answers
44 views

Is there a name for the function that gives me the signal of a number only?

I know the function that gives the absolute value of a number is called either absolute function or 'modulus' function, such as: $$ modulus(-6) = modulus(6) = 6 $$ Now, I want to name a function that ...
0
votes
1answer
21 views

Terminology — lying over something

I just came across reading something like this: 'Let $\phi\in \text{Gal}(L/K)$ lie above $Frob\in \text{Gal}(K^{un}/K)$.' Where $Frob$ is the Frobenius automorphism and $K^{un}$ is the maximal ...
5
votes
2answers
185 views

Two point topological space

Is there a standard name for the two point space with precisely one singleton being the only nontrivial open set? What are its most noteworthy categorical properties?
3
votes
1answer
23 views

Terminology - Limit doesn't exist

Take the following limit: $$ \lim_{x \to 2} \dfrac{x+2}{x-2} $$ This doesn't exist. My textbook says it doesn't because "The denominator approaches 0 (from both sides) while the numerator does not." ...
1
vote
0answers
27 views

What is the difference between perturbation theory and numerical analysis?

What is the difference between perturbation theory and numerical analysis? Both subjects are trying to obtain the approximate answer. What are they study specifically?
0
votes
0answers
19 views

Order on the set of partitions (terminology)

Let $S$ and $T$ be partitions of some set $U$. What is the name for the partition $\{ X\cap Y \mid X\in S, Y\in T, X\cap Y\ne\emptyset \}$? Should it be called the infimum of $S$ and $T$? meet of ...
0
votes
1answer
26 views

Name for shape defined by volume between two concentric spheres

Is there a proper name for a shape defined by the volume between two concentric spheres? My understanding is that, formally, a "sphere" is strictly a 2D surface and there's a formal term for volume ...
-1
votes
5answers
95 views

Why the term “countable”?

In my computer science theory class, we are discussing the concept of countability. I understand the concept, but the choice to use the word countability seems absolutely unintuitive to me. Why was ...
3
votes
0answers
45 views

A variant of projective objects?

Let $\mathcal{C}$ be an additive category. Is there a common name for objects $P \in \mathcal{C}$ with the property that $\hom(P,-) : \mathcal{C} \to \mathsf{Ab}$ is right exact, i.e. preserves all ...
2
votes
1answer
72 views

Is “connected, simply connected” Redundant?

Here are my definitions of "connected" and "simply connected." A topological space $X$ is connected if and only if it is not the union of two nonempty disjoint open sets. A topological space ...
4
votes
4answers
130 views

How do you read the symbol “$\in$”?

A variable in an equation may be replaced by any of the numbers in its domain. The resulting equation may be either true or false. Here is another way to show ...
0
votes
0answers
32 views

What's the mathematical name to scale a number to a new resolution

From a programmers background, i know what i need to accomplish, and how i should, but i don't know if there's a mathematical name for what i'm doing here... For examle, i have the number 5 in a ...
2
votes
2answers
56 views

Does the word 'ten' have a base?

My friends and I had a debate: "Does the word 'ten' have a base?" My Argument: 'ten' is only 10 in base 10 so if i have 10 objects, counting in base 10, when I get to the end of the list, I will ...
0
votes
1answer
32 views

Maximum/Maximal set

Maximum or maximal set with property $P$ When I was reading some textbooks, I noticed that I do not get the meaning of the following two phrases. ($P1$) $\quad$ maximum set with property $P$ ($P2$) ...
1
vote
1answer
50 views

How would you describe category $\mathsf{Rel}$?

I encountered two definitions for a category denoted by $\mathsf{Rel}$: Objects are pairs $\left(A,R\right)$ where $A$ is a set and $R$ a relation on $A$. Arrows in ...
0
votes
0answers
10 views

Name of the set of points equidistant from a line

I was reading about geometrical shapes in n-dimensional Euclidean spaces and programming some objects that would share some of their properties in different dimensions, like n-spheres. I had somewhere ...
5
votes
1answer
351 views

What does “s.t.” mean?

English is my second language and I have a question. What does "s.t." mean? $ \text{min} \quad f(x) = (x1−2)^2+(x2−1)^2 $ $ \text{s.t.}\qquad g_{1}(x) = x_{1} - 2x_{2} + 1 = 0 $ $ \qquad\qquad ...
0
votes
5answers
74 views

In probability: is there a name for 1-x or x-1?

I should frame this question in the context of dealing with probabilities: I've read the wikipedia entry on the multiplicative inverse: http://en.wikipedia.org/wiki/Multiplicative_inverse Where it ...
0
votes
1answer
29 views

Is there any special name for a $n$-torus made by products of hyperspheres?

I was wondering if there exist an accepted name for an $n$-torus made by the product of hyperspheres $\mathbb{S}^d$, that is for the following set: $$ ...
0
votes
1answer
36 views

What does it mean “sequence with infinite range”

I'm trying to understand this phrase Find a sequence with infinite range that converges only to $0$. What does it mean "sequence with infinite range"? Thanks
0
votes
0answers
8 views

Terminology for particular situations?

What might be the name for a situation where a Hermitian (complex) operator produces real values? Could it be inversion, or convolution or something of that sort? And can the reverse situation be ...
0
votes
2answers
22 views

Terminology - variant of a hypergraph

In a hypergraph, we have vertices $V$ and hyperedges $H$, where each hyperedge is a subset of $V$. Suppose that we would like the hyperedges to be (ordered) tuples, rather than subsets. Does this ...
0
votes
1answer
24 views

Does a graph of this type have a name?

Does a graph of this type have a name? When I say a "graph of this type" I mean where the scales on the axes aren't uniform all the way along.
2
votes
1answer
39 views

Is algebra over a set also algebra over a field?

During my studies I have come across two different notions of the term "algebra", namely algebra over a set and algebra over a field (the field its vector space always being Euclidean space in my ...
8
votes
4answers
294 views

What is linearity?

Once someone asked me the question "What is linearity?" in a proficiency exam. I went hot and cold all over. Although, I heard and even used the term linearity many many times, I had not really ...
0
votes
1answer
26 views

Need help to understand some terminology in discrete math

1) "Suppose that f is a function from set A to itself." 2) "(...)from the set of real numbers to itself." In these two sentences, what does "to itself" mean? Is this the same as saying that 1) is f: ...
0
votes
0answers
37 views

What's the right way to write big-O?

I always write $\mathcal{O}(n)$ (\mathcal{O}(n)). But I frequently see $O(n)$ (O(n)), probably because it's shorter and more ...
0
votes
0answers
22 views

“two sets differ” in vs by “exactly 1 element”, in both cases is symmetric implied?

When a mathematician says, "two sets differ in exactly 1 element", what precisely do they mean? Does, "two sets differ by exactly 1 element", mean something different? Given $ A = \{1,2,3\}, B = ...
0
votes
0answers
32 views

Terms for particular equivalence relation and partition?

Let $T$ be a set of sets. Let $\equiv$ be an equivalence relation on $\bigcup T$ defined by the formula $$a\equiv b \Leftrightarrow \forall X\in T:(a\in X\Leftrightarrow b\in X).$$ Let $S$ be a ...
0
votes
0answers
16 views

Term for “interval with a step size”

I'm looking for a term for "interval with a step size". Let's write such an "interval" as an interval-like tuple $I=[from, step, to]$. Then $I$ is defined as $I=\{x|x=from+n \cdot step, n \in ...
4
votes
1answer
43 views

How to call a shape (2D or 3D) that has no dents in it?

Is there a name for a shape that has no dents in it? The shape can exist in 2D or 3D space. It is best demonstrated with a picture: On the left is a shape that has no dents in it, and on the right ...
0
votes
1answer
42 views

What's the terminology for whether a number is positive or negative?

Is there a word for the quality of a number to be either positive or negative? Consider this question: What's the ... (sign/positivity/negativity, but a word that could describe either) of number x? ...
0
votes
2answers
53 views

Terminology for $1/(e^x+1)$?

$ \frac{1}{e^x+1} $ and $ \frac{e^x}{e^x+1} $ Just wonder if either of the above function has a term/name associated with it? Or they are just functions that look beautiful without names? Maybe they ...
0
votes
0answers
11 views

Is “nonanticipating” a measurability property of a function or something more?

I have been reading some operations research papers that throw in the term "nonanticipating" at key points in the exposition, but I can't figure out precisely what they mean. My best guess is that ...
3
votes
0answers
47 views

Why are centers, centralizers and normalizers called that way?

I know what they are, but where do the names come from?
5
votes
0answers
106 views

Have these (extremely simple) classes of algebraic structures been considered in the literature? If so, what are they called?

Questions. Have the following kinds algebraic structures been considered in the abstract algebra literature etc.? If so, what are they really called? (I have used made-up terminology for the sake ...
0
votes
1answer
18 views

Is this ODE linear?

Determine whether the given first order differential equation is linear in the following variables: $(y^2-1)dx+xdy=0$; in x and y I'm pretty confused here. I've seen $\frac{dy}{dx}$ but what do $dy$ ...
2
votes
1answer
41 views

Is this an ordinary differential equation?

If a differential equation contains only ordinary derivatives of one or more functions with respect to a single independent variable it is said to be an ordinary differential equation (ODE). If ...
0
votes
0answers
25 views

For every pair of vertexes there is at most one path

A directed graph such that for every pair $(A;B)$ of vertexes there is at most one path from $A$ to $B$, is there are name for this concept? @Ishfaaq: Your answer is wrong, see such a digraph which ...
0
votes
0answers
34 views

In linear algebra, what is the word used to state that two linear equations are the same line?

If we have to solve a system of linear equations with two linear equations. What is it called if both of these two lines are the same? I.e. the first line is $x+y=1$ and the second line is ...
0
votes
1answer
14 views

Signal “representation” terminology

A paper I'm reading now defines invariant signal "representations" as those functions $\Phi$ of signals $x$ in a Hilbert space such that $\Phi(g\cdot x) = \Phi(x)$ where $g\cdot x$ is the action of ...
0
votes
1answer
30 views

The proper term to describe a category of geometric shapes.

I'm looking for geometric terminology that would describe this kind of shape, if there is a term for it. Picture any arbitrary closed 2D shape. Picture the smallest circle that will completely contain ...
1
vote
1answer
48 views

Definition Fixed Element

I am looking for the definition of a "fixed element". The context is "Let G be a group and let a be one fixed element of $G$. Show that $H_a = \{x \in G | xa=ax \}$ is a subgroup of $G$." Thanks.
1
vote
0answers
32 views

operator vs operation vs function vs procedure vs algorithm

I have a vague understanding of what operator, operation, function, procedure, algorithm mean in general. I am heavily biased towards computer science. Do you agree with them? What are the generally ...
2
votes
1answer
29 views

Is there a name for spaces that always have local sections?

Given a continuous map $p:E \rightarrow B$ Suppose for every point $b \in B$ and a point $x \in p^{-1}b$ in the fibre of it, there is an open set $V$ of $B$ that contains the point $b$ such that ...
1
vote
0answers
30 views

Eigenvalues that are functions

Let us have the Laplacian on a compact manifold $M$. Suppose I have some equation of the form $$-\Delta u(x) = f(x)u(x).$$ If $f \equiv c$ were a constant, this would be an eigenvalue problem ...
0
votes
0answers
24 views

The space of alternating multilinear forms

I was just wondering if there is a standard (or even just usual) notation for the space of alternating $k$-linear forms on an $F$-vector space. I know that this space is naturally isomorphic to the ...
0
votes
1answer
17 views

Number of variables and dimension of a function

Why is a function $f(x)$ called a single-variable function if it has coordinates represented by $x$ and $y$? Can it be called a 1D function if its plot is 2D? Subsequently, can two-variable functions ...